Question

YZ and YX are tangent from the external point Y on a circle with centre O of angle XOY =50 degree, then find angel XYZ. ​

Answer 1

Step-by-step explanation:

From the figure, there is an external point X from where two tangents, XP and XQ, are drawn to the circle.

XP=XQ

(The lengths of the tangents drawn from an external point to the circle are equal.)

Similarly,

AP=AR

BQ=BR

XP=XA+AP --------- (1)

XQ=XB+BQ --------- (2)

By substituting AP=AR in equation (1) and BQ=BR in equation (2), we get

XP=XA+AR

XQ=XB+BR

Since the tangents XP and XQ are equal, we get

XA+AR=XB+BR.